NBT Logical Reasoning & Problem Solving

Question 1

If all roses are flowers and some flowers fade quickly, can we conclude that some roses fade quickly?

Accepted Answer

No, we cannot directly conclude that.

Answer

This is an example of an invalid syllogism. While all roses are flowers, and some flowers fade quickly, the 'some flowers' that fade quickly might not include any roses. There is no logical link to guarantee an overlap between the specific subset of 'roses' and the subset of 'flowers that fade quickly,' so we cannot directly conclude that some roses fade quickly.

Question 2

What is the next number in the sequence: 2, 6, 12, 20, ?

Accepted Answer

30.

Answer

To find the next number, we identify the pattern in the differences between consecutive terms. The differences are: 6-2=4, 12-6=6, 20-12=8. This shows an increasing difference of +2 each time. Following this pattern, the next difference should be 8+2=10, so the next number in the sequence is 20+10=30.

Question 3

What is the logical conclusion of this syllogism? All humans are mortal. Socrates is a human.

Accepted Answer

Socrates is mortal.

Answer

This is a classic example of a valid deductive syllogism. The first premise establishes a general truth: 'All humans are mortal.' The second premise identifies a specific case that fits this general category: 'Socrates is a human.' Therefore, the logical conclusion is that Socrates must possess the characteristic attributed to all humans, which is mortality.

Question 4

Which of the following conclusions is valid based on the statement: All cats are mammals, and all mammals have fur?

Accepted Answer

All cats have fur.

Answer

This conclusion follows directly from the transitive property of logical statements. If 'All cats are mammals' and 'All mammals have fur,' then it logically follows that the characteristic of having fur applies to all members of the 'cats' category. Since cats are a subset of mammals, and all mammals have fur, all cats must also have fur.

Question 5

What is the next number in the sequence: 1, 4, 9, 16, ?

Accepted Answer

25.

Answer

This sequence consists of perfect squares. Each term is the square of its position in the sequence: 1 is 1², 4 is 2², 9 is 3², and 16 is 4². Therefore, the next number in the sequence, which is the fifth term, will be 5², which equals 25.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT Logical Reasoning & Problem Solving